The invention relates to the field of quantum computing, and particularly to superconducting quantum computing and read-out for flux-biased qubits.
Description Of Background
Quantum computing is a new paradigm of computing requiring fundamentally fewer resources to solve certain computationally interesting problems compared to classical computing. This feat is enabled by several peculiar properties found in quantum systems that are impossible to achieve in classical systems: the ability for a quantum system to be in a superposition of several of its eigenstates and the ability for several quantum systems to be entangled with one another.
The requirements for building a large-scale quantum computer, however, are more intricate than the properties of superposition and entanglement alone. In fact, there is a set of requirements that must be fulfilled in order to build a practical quantum computer. One requirement is to have a system of quantum bits (qubits) which can be initialized to a known state. Another requirement is the ability to manipulate this state by applying single and multi-qubit gate operations such that any arbitrary logic operation can be implemented. Finally, the outcome of the computation must be measured through known techniques.
Although these requirements sound trivial at first, in practice it is significantly more challenging to find or design an appropriate system that satisfies these conditions simultaneously. For a quantum system to retain the delicately created superposition and entangled states for sufficiently long times (called coherence times) it must be well isolated from the environment. However, in order to manipulate the quantum system according to the steps of the desired algorithm it must inherently also be coupled to the external environment thereby introducing noise mechanisms that reduce coherence times. It is precisely these opposing requirements that represent a challenge for theorists and experimentalists alike to design an appropriate system.
The most favorable feature of superconducting qubits is their compatibility with standard modern Silicon micro fabrication techniques. It is therefore believed that the fabrication of thousands or millions of qubits on a chip is possible. In addition it is hoped that these may be integrated with other silicon or other semiconductor devices.
Even for superconducting qubits, it remains challenging to design a circuit that gives rise to a quantum mechanical system useful as a qubit. Several designs emerged over the years and generally fit into three categories: charge qubits, flux qubits, and phase qubits (or hybrid designs).
The names for the different types of qubits are loosely related to the physically differing quantities for the logical |0TM and |1TM states. For example, the charge qubit derived its name based on the presence of an excess Cooper pair (|1TM state) or the lack of one (|0TM state). This is similar to classical bits where the logical states 0 and 1 are also physically distinct states. Over the past several years the correlation between the qubit name and physical interpretation of the quantum states became more ambiguous. Careful device engineering has lead to qubits whose logical states are physically less distinct. Because it is more difficult to distinguish the two states, the impact of the residual coupling to the environment is also reduced thereby making the coherence time of the qubits longer. As a result, however, a desired measurement of the device is also more cumbersome.
A desired measurement is defined as determining which of the logical quantum states is occupied. There are a variety of ways this can be achieved. In the so-called quantum non-demolition (QND) measurements, the measurement is achieved without projecting the state out of the qubit manifold (or “destroying” the qubit) and the system remains in the state that has been measured, up to the coherence time if it is the excited state. This has the advantage that resetting the qubit into a desired state is straightforward but the measurement times generally increase and the engineering of such a measurement is also often quite challenging.
The measurement can also be achieved in a different way, often in two separate steps. In the first step, one of the two states of the qubit is selectively projected onto a different state that is physically very distinct from the remaining one. After this step, the qubit is, as far as the wave function of the system is concerned, already measured and additional decoherence or strong coupling to the environment is usually no longer detrimental provided both states are a local ground state. The step can be referred to as the actual ‘measurement’. In the second step, it is now possible to determine what happened during the measurement, which can be referred to as the ‘read-out’. The ‘read-out’ simply determines which state the qubit occupies, which then reveals the state of the qubit before ‘measurement’. It is sometimes possible to perform the read-out long after measurement given that the two possible outcomes are macroscopically stable states.
For example, suppose that the ‘measurement’ projects the qubit from state |0TM to state |ATM and state |1TM to state |BTM with 100% accuracy. Both |ATM and |BTM are very distinct states and locally correspond to a quasi stable state. The read-out now determines if the qubit is in state |ATM or |BTM which then reveals whether or not the qubit was in |0TM or |1TM prior to measurement.
Currently, all superconducting qubit measurement and/or read-out designs either require a relatively strong coupling of the qubit to other nonlinear superconducting circuit elements such as a superconducting quantum interference device (SQUID), or are based on other techniques that indirectly probe the qubit state.
Most designs rely on coupling the qubit sufficiently strongly to a SQUID (either DC or RF) and then measuring the response of the SQUID either by using direct current or microwave techniques. By coupling the qubit strongly to a SQUID new potential decoherence channels are introduced. The SQUID is inherently also a quantum mechanical object and can be characterized by a quality factor. Because the SQUID is itself coupled to external bias leads it generally has low quality factors, which the qubit is exposed to via the coupling mechanism. Although the extent of the residual coupling can be minimized, the procedure requires careful calibration or design layouts and even small deviations can negatively impact qubit performance.
By using direct current techniques to measure the response of the SQUID, the SQUID switches to a voltage state which introduces heating around the qubit adding to decoherence of the qubit in subsequent experiments and/or slowing down the experimental repetition rate. Using microwave techniques to measure the response of the SQUID, the measurement time is often decreased and no heat is dissipated around the qubit. However, the SQUID remains in place and may cause decoherence as described earlier.
A few designs do not rely on coupling to an external SQUID in order to measure the state of the qubit. One well-known design includes coupling the qubit to a superconducting coplanar waveguide resonator. The measurement is done via phase detection of a microwave signal passed through the resonator because the phase of the transmitted signal depends on the state of the qubit. Although no external SQUID is required, a relatively strong coupling between the qubit and a reasonably large superconducting resonator is still needed. Furthermore, this measurement probes the qubit state indirectly by determining the transmission through another circuit element, namely a carefully engineered coplanar waveguide resonator. Finally, it is also not clear how to couple multiple qubits together in a straightforward manner.
Another well-known design also couples the qubit to an external superconducting resonator. However, in this case the qubit state is measured by applying a microwave signal that is tuned to the energy difference between one of the qubit states and a third auxiliary level. If that qubit state is populated, the system undergoes Rabi oscillations between that and the auxiliary level. By tuning the power of the microwave signal it is possible to match the Rabi frequency to the frequency of the external superconducting resonator. As a result, the external resonator is driven by the Rabi flopping which gives rise to a measurable voltage signal. Therefore, the qubit measurement is a voltage measurement across the external resonator. This technique is also an indirect measurement of the qubit state by probing the response of another superconducting circuit element, and requires cumbersome calibrations.